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lme4 vs. HLM (program) - differences in estimation?

Douglas Bates
On Tue, Nov 18, 2008 at 11:02 AM, Felix Sch?nbrodt <nicebread at gmx.net> wrote:
That formula is not incorrect but it is a bit redundant.  In the R
formula notation the ':' operator creates an interaction and the '*'
operator is used to cross effects.  Thus meanses*ses expands to
meanses + ses + meanses:ses
Does the HLM specification allow for correlation of the random effects
within ID group?  The lmer specification does.
The criterion, either the log-likelihood for ML estimates or the REML
criterion for REML estimates, is defined as a property of the data and
the model.  The issue I was discussing there is how to evaluate the
log-likelihood or the REML criterion given the data, the model and
values of the parameters.  Solving a penalized least squares problem
or a generalized least squares problem is just a step in the
evaluation.  Both paths should give the same answer.  The reasons I
prefer the penalized least squares approach have to do with accuracy,
reliability and speed as well as generality of the approach.

I think it will be more important to check that the model
specifications are the same and that you are using the same criterion.
 The default criterion for lmer is REML.  I don't know what the
default criterion for HLM is.
I'm not sure what that would mean.  To a statistician "Bayesian
Estimation" would be associated with Bayesian representations of
models in which the parameters are regarded as random variables.  The
estimation criterion would change from the likelihood (or a related
criterion like the REML criterion) to maximizing the "posterior
density" of the parameters.  Because the posterior density depends on
the likelihood and on the prior density you must specify both the
probability model and prior densities to be able to define the
estimates.

At least that is the statistician's view of Bayesian estimation.  In
some fields, like machine learning, the adjective Bayesian is applied
to any algorithm that seems remotely related to a probability model.
For example, if you check how movie ratings are calculated at imdb.com
they use what they term is a Bayesian algorithm which, in their case,
means that they use a weighted average of the actual votes for the
movie and a typical vote so that a movie that is highly rated by very
few people doesn't suddenly become their number 1 rated movie of all
time.  Just saying it is Bayesian doesn't define the answer.  You need
to specify the probability model.

I would check two things: does HLM estimate two variances and a
covariance for the random effects and is it using the REML criterion
or the ML criterion.

Thread (10 messages)

Felix Schönbrodt lme4 vs. HLM (program) - differences in estimation? Nov 18 Doran, Harold lme4 vs. HLM (program) - differences in estimation? Nov 18 Felix Schönbrodt lme4 vs. HLM (program) - differences in estimation? Nov 18 Doran, Harold lme4 vs. HLM (program) - differences in estimation? Nov 18 Douglas Bates lme4 vs. HLM (program) - differences in estimation? Nov 18 Douglas Bates lme4 vs. HLM (program) - differences in estimation? Nov 18 Doran, Harold lme4 vs. HLM (program) - differences in estimation? Nov 18 Felix Schönbrodt lme4 vs. HLM (program) - differences in estimation? Nov 18 Doran, Harold lme4 vs. HLM (program) - differences in estimation? Nov 18 Douglas Bates lme4 vs. HLM (program) - differences in estimation? Nov 18